On the Robustness to Misspecification of α-posteriors and Their Variational Approximations
Authors: Marco Avella Medina, José Luis Montiel Olea, Cynthia Rush, Amilcar Velez
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We contribute to this growing literature by investigating the robustness to misspecification of α-posteriors and their variational approximations, with a focus on low-dimensional, parametric models. Our analysis motivated by the seminal work of Gustafson (2001) is based on a simple idea. We establish a Bernstein von Mises (Bv M) theorem in total variation distance for α-posteriors (Theorem 1) and for their (Gaussian mean-field) variational approximations (Theorem 2). We also extend the results of Li et al. (2019), who establish the Bv M theorem for α-posteriors under a weaker norm but under more primitive conditions. The paper heavily relies on mathematical derivations, theorems, and asymptotic approximations (Bv M theorem) to analyze the theoretical properties of α-posteriors. While Section 5 includes 'Numerical Experiments,' these are illustrative examples for a theoretical model rather than empirical validation against real-world data with performance metrics. |
| Researcher Affiliation | Academia | Marco Avella Medina EMAIL Department of Statistics Columbia University New York, NY 10027, USA; Jos e Luis Montiel Olea EMAIL Department of Economics Columbia University New York, NY 10027, USA; Cynthia Rush EMAIL Department of Statistics Columbia University New York, NY 10027, USA; Amilcar Velez EMAIL Department of Economics Northwestern University Evanston, IL 60208, USA. All listed affiliations are universities. |
| Pseudocode | No | The paper describes mathematical frameworks and theorems using standard notation and equations. There are no explicit sections or figures labeled 'Pseudocode' or 'Algorithm', nor are there any structured, code-like procedural blocks. |
| Open Source Code | No | The paper does not contain any explicit statement about releasing source code for the described methodology, nor does it provide a link to a code repository. |
| Open Datasets | No | The paper uses a simulated example (linear regression model with omitted variables) for its numerical experiments (Section 5), rather than an existing publicly available dataset. The data is generated according to specified distributions and parameters, not accessed from a public source. |
| Dataset Splits | No | The paper's numerical experiments involve a simulated linear regression model where data is generated for various sample sizes (n = {1000, 100000, ∞}). There is no mention of splitting an existing dataset into training, validation, or test sets as the data is generated on demand for illustrative purposes. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run the numerical experiments, such as GPU or CPU models, or memory specifications. It only mentions using 'R' for generating Gaussian draws. |
| Software Dependencies | No | The paper mentions using 'R' for generating Gaussian draws in the numerical experiments (Section 5.5). However, it does not specify a version number for R or any other software libraries or dependencies used, which is required for reproducible description. |
| Experiment Setup | Yes | In Section 5.5 'Numerical Experiments', the paper specifies various parameters for the simulated model: 'p = 2 and d = 1', 'γ0 = 5 and set θ0 = ( -0.626, 0.184)', 'σϵ = 2', and the covariance matrix Σ for (Wi,1, Wi,2, Zi) with 'ρ = 1/2'. It also states 'ϵn = 10/n so that nϵn → ϵ = 10' for simulations. These details constitute the experimental setup for the numerical illustration. |